There'll be some big political changes taking place inside the inner chambers of the EU over the next few months, as officials decide who'll take key roles at the helm of the euro zone bloc.

Behind closed doors some names have started to emerge with the incumbents set to step down at the end of the year. The roles up for grabs will be the president of the Eurogroup (which brings together the finance ministers of the 19 countries that share the euro) and the president of the Euro Working Group (a less-known position, which decides the agenda of the Eurogroup).

Why do we care?

Both positions are key for the stability and future of the euro zone (the monetary bloc of 19 nations), and will oversee new rules that could be applied to European banks and could affect how Greece's debt is restructured.

Furthermore, they will influence who will take the presidency and vice-presidency of the European Central Bank (ECB). In Europe, there's always a "battle" of nationalities between member states when deciding which seat goes to whom.

The Eurogroup and Euro Working Group are "spiders in the web and often mediators between different countries and different interests," Carsten Brzeski, chief euro zone economist at ING, told CNBC via email.

Who will replace Dijsselbloem?

Emmanuel Dunand | AFP | Getty Images

Eurogroup President and Dutch Finance Minister Jeroen Dijsselbloem

Jeroen Dijsselbloem is the current chief of the Eurogroup and the decision on who will replace him is expected at the start of December.

The Dutch politician is leaving in January and one of the 19 sitting finance ministers will take his role. At the moment there are five names being mentioned the most: the Spanish Finance Minister Luis de Guindos, the Portuguese Finance Minister Mario Centeno, the Slovak Finance Minister Peter Kazimir, the French Finance Minister Bruno Le Maire and the Luxembourg Finance Minister Pierre Gramegna.

Luis de Guindos has previously run against Dijsselbloem in the last election for the presidency, but failed to get enough support from his colleagues. He is also often mentioned as one of the potential names to fulfill the vice-presidency of the ECB and therefore may shy away from the Eurogroup.

Mario Centeno didn't rule out the Eurogroup presidency in an interview with CNBC back in May. In his favor is the fact that he's from the Socialist Party in Portugal, because currently the majority of the big European positions are in the hands of the center-right and EU officials tend to strike a balance between nationalities and political affiliations when distributing European roles.

Peter Kazimir is also from the left but he is often viewed, just like Dijsselbloem, as a center-right man. He has been one of the most critical ministers of Greece's bailout program, incentivizing structural reforms and tough economic measures. This could hurt his chances if indeed ministers look for a president from the "traditional" left.

The same applies to France's Le Maire. It's not a secret that the French President Emmanuel Macron is keen on securing some key roles for France. The skills of Bruno Le Maire are indeed a plus, such as his fluency in German, but he is also perceived as a right-wing politician. He belonged to the Les Republicains party and is in charge of fulfilling deep reforms in France.

Socialist parties across Europe haven't had great results in the past few elections and have struggled to get into government. Therefore there aren't many options from the left that could take the Eurogroup presidency. In this case, Pierre Gramegna from Luxembourg could emerge as the winner. He belongs to one of the founding members of the European Union and is from a liberal party.

What about the Euro Working Group?

The group has been in the hands of an Austrian man, Thomas Weiser, who has been crucial to overcome many stones in the Greek bailout program.

There seem to be two countries potentially taking this role: France and Finland. However, this role requires moving to Brussels and the French representative doesn't seem keen.

So what about the ECB?

It is still early to discuss the future of the ECB, given that the mandate for the current president comes to an end only in October 2019. Before that, Europe will have to choose the vice-president of the ECB – currently in the hands of Vitor Constancio. The Portuguese man will end his reign in May of next year.

"In the entire musical chair game of upcoming nominations for European top jobs, the vice-presidency at the ECB is important. It could be a counterweight to the president. It could also be a way to give a smaller euro zone country a top job," Brzeski said.

Again, Spain's de Guindos is seen as a potential candidate.

What's known at the moment is that it's not certain that Germany will get the presidency of the ECB, despite many media reports pointing towards Jens Weidmann, the governor of the German central bank, as the most likely name to take the most important seat at the ECB.

"For Germany, or at least for the German public, the ECB presidency is highly symbolic," Brzeski said.

"Even though a German ECB president could be a bit too much of German dominance in Europe, Germany could use the ECB presidency as change for agreeing to a set of more controversial measures when it comes to further euro zone integration," Brzeski added.

However, some argue that Germany will want to have someone from outside its country to put the blame on whenever the course of monetary policy doesn't fit its interests.